What is the greatest common factor of $35y^{4}$, $14y^{4}$, and $63y^{4}$ ?
Explanation: Let's factor each monomial to its prime factors: $\begin{aligned} 35y^{4}&=(5)(7)(y)(y)(y)(y) \\\\ 14y^{4}&=(2)(7)(y)(y)(y)(y) \\\\ 63y^{4}&=(3)(3)(7)(y)(y)(y)(y) \end{aligned}$ We want the largest set of factors that's included in all three monomials. All of the monomials have one factor of $ 7$ and four factors of $ y$ : $\begin{aligned} 35y^{4}&=(5)( 7)( y)( y)( y)( y) \\\\ 14y^{4}&=(2)( 7)( y)( y)( y)( y) \\\\ 63y^{4}&=(3)(3)( 7)( y)( y)( y)( y) \end{aligned}$ This is the greatest common factor: $( 7)( y)( y)( y)( y)=7y^{4}$